Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...

of star-forming material. Here we take the above star-formation rate to be
constant over a Hubble time tH, where
tH(z) 2 × 10 8
1 + z
yr
21
−3/2
, (6.6)
evaluated at the relevant redshift. We assume that each star quickly dies as a
PISN with ESN = 10 52 erg, appropriate for a 200 M⊙ star (Heger and Woosley
2002), ten percent of which is transformed into CR energy (e.g. Ruderman
1974). The value of ten percent is derived from Milky Way (MW) energetics,
and here we have simply extrapolated this to PISNe. Very little is known
about what value of pCR applies to PISNe specifically, so assuming their shock
structure to be similar to local SNe appears to be a reasonable first guess.
We choose 1/500 M⊙ for fPISN, so that there is one PISN for every 500 M⊙ of
star-forming material. This implies that somewhat less than half of the star
forming mass falls within the PISN range.
Compared to PISNe, the usual core-collapse SNe (CCSNe) thought
to accelerate CRs in the Milky Way have an explosion energy that is lower
by about an order of magnitude. However, the masses of their progenitor
stars are also much lower, ranging from ∼ 10 − 40 M⊙. Thus, if we have an
IMF extending to this lower mass range, there will be approximately an order
of magnitude more SNe per unit mass of star-forming material. However,
because ESN for low-mass (∼ 10 M⊙) CCSNe progenitors will be lower by a
similar amount, these two effects may cancel out and result in a total UCR
that is comparable to the PISN case. Furthermore, the difference in shock
velocities, ush, between a PISN and a CCSN should not be more than a factor
of a few. Though CCSNe have a lower explosion energy, this energy is used
to accelerate roughly ten times less ejected mass, Mej, than in a PISN. Simple
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